The Poisson kernel of positively curved manifolds

DOI10.1016/0022-1236(81)90015-XzbMath0507.58046OpenAlexW2055064985MaRDI QIDQ1837458

Nicholas Th. Varopoulos

Publication date: 1981

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(81)90015-x

zbMATH Keywords

Ricci curvaturePoisson semigroupPoisson functionHarnack type inequalityLaplace- Beltrami operatorHardy-Littlewood function

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (25)

Bounded harmonic functions and positive Ricci curvature ⋮ Hardy-Littlewood theory for semigroups ⋮ Heat kernel on smooth metric measure spaces and applications ⋮ On the parabolic kernel of the Schrödinger operator ⋮ Sharp estimates for capacities and applications to symmetric diffusions ⋮ Three circles theorems for harmonic functions ⋮ Stable solutions of elliptic equations on Riemannian manifolds ⋮ New monotonicity formulas for Ricci curvature and applications. I ⋮ Gap theorems for locally conformally flat manifolds ⋮ Sharp Gaussian upper bounds for Schrödinger heat kernel on gradient shrinking Ricci solitons ⋮ From holography to the geometry of the spacetime ⋮ Ricci curvature and monotonicity for harmonic functions ⋮ Green's functions on positively curved manifolds ⋮ Volume growth, Green's functions, and parabolicity of ends ⋮ A note on Liouville type theorem of elliptic inequality \(\delta u+u^\sigma\leqslant 0\) on Riemannian manifolds ⋮ The growth rate of harmonic functions ⋮ Boundary behavior of harmonic functions on manifolds ⋮ Integral of scalar curvature on non-parabolic manifolds ⋮ A note on the existence of positive Green's function ⋮ Canonical identification at infinity for Ricci-flat manifolds ⋮ Geometry of positive scalar curvature on complete manifold ⋮ Green's functions on positively curved manifolds. II ⋮ On the Discrete Spectrum of Generalized Quantum Tubes ⋮ Analysis of the Laplacian on a complete Riemannian manifold ⋮ A criterion of nonparabolicity by the Ricci curvature

Cites Work

• Aspects of probabilistic Littlewood-Paley theory
• Eigenvalue comparison theorems and its geometric applications
• Théoremes de comparaison en géométrie Riemannienne
• On the heat kernel of a complete Riemannian manifold
• Lectures on stochastic processes. Notes by K. Muralidhara Rao. Reissued ed
• The relation between the Laplacian and the diameter for manifolds of non- negative curvature
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
• The splitting theorem for manifolds of nonnegative Ricci curvature
• $C^\infty$ approximations of convex, subharmonic, and plurisubharmonic functions
• Conditional brownian motion and the boundary limits of harmonic functions
• Harmonic functions on complete riemannian manifolds
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
• A Maximal Theorem
• A Maximal Function Characterization of the Class H p
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The Poisson kernel of positively curved manifolds